1. Combining Functions
Section 1.7

2. Objectives
Determine the domain and range (where possible) of a function given as an equation.
Add, subtract, multiply, and/or divide function.
State the domain two function combined in an arithmetic method.
Put together two (or more) functions using composition.
Determine the value of the composition of two (or more) functions given the graphs of the functions.
Determine the value of the composition of two (or more) function given the equations of the functions.
State the domain two function combined through composition.

3. Objectives
Decompose the composition of two functions into it constituent functions.
Solve a word problem involving the composition of functions.

4. Vocabulary
domain
range
function composition

5. Domain Questions Does the function have a denominator?
Does the function have a square or even root?
Does the function have a log or ln in it?
Did the function arise from finding an inverse?
Is this a “real world” problem?

6. Find the domain of the function:

7. Find the domain of the function:

8. Find the domain of the function:

9. Find the domain of the function:

10. Given the functions and find each of the following:

11. Given the functions and find the domain of each of the following:

12. For the functions f(x) and g(x) are given in the graph below
For the functions f(x) and g(x) are given in the graph below.  Find the indicated corresponding function values

13. Given the functions and find each of each of the following:

14. Given the functions and find each of the following:

15. Given the functions and find the domain of each of the following:

16. For the functions f(x) and g(x) are given in the graph below
For the functions f(x) and g(x) are given in the graph below.  Find the indicated corresponding function values

17. Express the function in the form . If , find g(x).

18. A spherical weather balloon is being inflated
A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 9 cm per second. Express the surface area of the balloon as a function of time t (in seconds).